CAT Previous Year Questions : Profit, Loss & Discount (June 24) - CAT MCQ

Let A be the cost price of object A and B be the cost price of object B.
Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B.
Therefore, 1.2 × A = 0.9 × B
4 A = 3 B
B = 4/3 A
To sell object B at a profit of 10%, the selling price of B must be 1.1 B or 11/10 B
Object A is sold at the same price as object B, that is, 
The profit obtained on object A in such a trade will be 46.66% or nearly 47%.

“Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit.”
This means, Minu purchased the glasses at Rs.1000 and sold them to Kanu at Rs.1200.
Minu made a profit of Rs. 200 so far.
“Then, Kanu sells it back to Minu at 20% loss.”
This means, Kanu sold the glasses back to Minu at 80% of 1200 = Rs. 960
“Finally, Minu sells the same pair of sunglasses to Tanu. … the total profit made by Minu from all her transactions is Rs.500”
This means, Minu has to make a further profit of Rs. 300. She achieves this by selling the glasses back to Tanu at 960 + 300 = Rs.1260
So the profit % in the transaction is 

Let's say the merchant paid for 95×100 m .
He pays 95 × 100 × 100 rupees and gets 95 × 105 m of cloth.
(because, he pays Rs. 100/meter and gets 5% extra cloth)
He sells 95 cm of the cloth at Rs. 104.5 (5% discounted on Rs. 110)
So, the total money collected by the merchant will be  


This means, the profit percentage is 15.5%

Ankita had 4 kg cashews, 14 kg peanuts and 6 kg almonds.
In all, she had 24 kgs of nuts to sell. Let us assume the average buying price of these nuts is x rupees per kg.
Average buying price means, Whatever the per kg cost of cashews, peanuts and almonds is, when you mix 4 kg cashews, 14 kg peanuts and 6 kg almonds and get 24 kgs of nuts, let's assume each kg of nuts cost x rupees per kg.
Ankita planned to make a total profit of ₹1752 by selling these 24 kgs of nuts.
That means, she planned on making a profit of 1752/24 = ₹73 on these 24 kgs of nuts.
So the marked price of these 24 kgs of nuts is ₹‘x + 73’ per kg.
She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744.
This means,
4(x + 73) + 0.8 * 20(x + 73) = 24 x + 744
716 = 4x
x = 179
That means the buying price of 24 kgs of these nuts is 24x = 24(179) = ₹4296
In other words, the buying price of 4 kg cashews, 14 kg peanuts and 6 kg almonds is ₹4296.
We are told that “the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds.”
7C = 30 P = 9 A
Where C, P and A are the per kg buying costs of Cashews, Peanuts and Almonds respectively.
Let 7C = 30 P = 9 A = 630k
C = 90k
P = 21k
A = 70k
We know that, the buying price of 4 kg cashews, 14 kg peanuts and 6 kg almonds is ₹4296.
4 C + 14 P + 6 A = 4296
4 (90k) + 14 (21k) + 6 (70k) = 4296
360k + 294k + 420k = 1074k = 4296
k = 4
A = 70k = 280
The buying price of Cashews is ₹280 per kg.
The total money spent on Cashews is 6C = ₹1680

Let the Cost Price of Juice be rupees x per kg.
Since the Cost Price of Syrup is 20% less than the Cost Price of Juice, Cost Price of Syrup is 0.8x per kg.
Total Cost Price of Syrup = 110 * 0.8 x = 88 x
Total Coat Price of Juice = 120 * x = 120x
Total Cost Price = 88x + 120x = 208x
Since the Overall Profit Percentage is 64%.
Total Profit = 0.64(208x) = 133.12x

The profit generated on selling 10 kgs of Syrup which costs 0.8x rupees per kg at 10% Profit = 0.1 * 10 * 0.8x = 0.8x
The profit generated on selling 20 kgs of Juice which costs x rupees per kg at 20% Profit = 0.2 * 20 * x = 4x
The remaining profit (133.12x - (0.8x + 4x) = 128.32x) is generated by selling 100 kgs of Syrup and 100 kgs of Juice at ₹ 308.32 per kg.
The total Selling Price of 100 kgs of Syrup and 100 kgs of Juice is 200 * 308.32 = 2(30832)
Cost Price of 100 kgs of Syrup = 0.8x * 100 = 80x
Cost Price of 100 kgs of Juice = x * 100 = 100x
Total Cost Price = 80x + 100x = 180x
Profit = Selling Price - Cost Price
128.32x = 2(30832) - 180x
308.32x = 2(30832)
x = 200
Cost Price of Syrup per kg = 0.8 x = 0.8(200) = ₹160 per kg.

Considering the three kinds of tea are A, B, and C.
The price of kind A = Rs 800 per kg.
The price of kind B = Rs 500 per kg.
The price of kind C = Rs 300 per kg.
They were mixed in the ratio of 2 : 3: 5.
1/6 of the total mixture is sold for Rs 700 per kg.
Assuming the ratio of mixture to A = 12kg, B = 18kg, C =30 kg.
The total cost price is 800 x 12 + 500 x 18 + 300 x 30 = Rs 27600.
Selling 1/6 which is 10kg for Rs 700/kg the revenue earned is Rs 7000.
In order to have an overall profit of 50 percent on Rs 27600.
Thes selling price of the 60 kg is Rs 27600 x 1.5 = Rs 41400.
Hence he must sell the remaining 50 kg mixture for Rs 41400 - Rs 7000 = 34400.
Hence the price per kg is Rs 34400/50 = Rs 688

Let the amount invested by Anil Bobby and Chintu be x, y, and z.
Considering x + y + z = 100 x p.
Given Anil's share was 70 percent = 70 x p.
As per the information provided :
His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%.
Since the profits are distributed in the ratio of their investments :
With a 3% decrease in the profits the value of profit earned by A decreased by Rs 420 which was 70 percent of the total invested.
Hence for all three of them would be combinedly losing 
Hence 3 percent profit was equivalent to  Rs 600.
The initial investment is equivalent to Rs 20000.
This is the total amount invested.
Chintu's profit share increased by Rs 80 when the profit percentage increased by 2 %. A 2 percent increase in profit is equivalent to Rs 20000*2/100 = Rs 400.
Of which Rs 80 is earned by Chintu which is 20% of the total Rs 400.
Hence he invested 20% of the total amount.
Bobby invested the other 10 percent.
10 percent of Rs 20000 = Rs 2000

Profit per boarder = Total profit / Number of boarders.
Let the number of boarders be n.
Profit/boarder = 1600 - (Total cost/n)
Let the total cost be a + bn, where a = fixed, and b is the variable additional cost per boarder.
Profit/boarder = 1600 - (a + bn)/n
Profit/boarder = 1600 - a/n - b
1600 - a/50 - b = 200
1600 - a/75 - b = 250
Solving, we get a = 7500, and b = 1250
Hence, total profit with 80 people = 80 ( 1600 - 7500/80 - 1250) = 80 (350 - 7500/80)
= 28000 - 7500 = Rs. 20500

Using Alligation Rule, the ratio of cost prices of desktop and laptop will be

i.e., 2: 3
∴ The cost of desktop = 2/5 x 50000 = 20,000

Let the cost price and marked price of each toy be c and m respectively. 
Overall selling price = 
Given, 110% of 12c = 8.8m
⇒ c = 2m/3
Overall CP = 12 x 2m/3 = i.e. 8m
Required profit percentage = 
= 50%